A bug is placed at one corner of a wire frame in the shape of a cube. At the diagonally opposite corner is a piece of sugar.

The bug crawls along the 12 wires of the frame searching for the sugar. At each of the 8 corners the bug randomly chooses one a wire to follow next with the additional rule that it can never cross the same wire twice.

What is the probability that it will dead-end by reaching a corner with no available wires? In the case where it does reach the sugar, what is the expected number of edges the bug traverses?

(i) The required probability is 0.21875

Edited on November 28, 2023, 5:30 am

Posted by K Sengupta on 2023-11-28 03:15:59